It ends with him hoping- no false modesty about our Bob- that his own name will live for ever. When Shakespeare does that sort of thing he gets away with it. When Southey does it, well....
Poor Southey; he is remembered, but it's mainly as the first generation romantic poet it's safe to disregard- or- in other words as the chap who isn't as good as Wordsworth and Coleridge. Byron took a terrific swipe at him for greasing up to royalty. Flytings are terrible things. The poet who loses is stuck in the shit forever.
He wasn't a bad poet, just a moderately decent one. There's a poem about the Battle of Blenheim which- though rather heavy-handed- deserves to be read.